M-J. Yvonne Ou

TL;DR: The features and capabilities of MADNESS are described and some current applications in chemistry and several areas of physics are discussed.

TL;DR: The MADNESS (multiresolution adaptive numerical environment for scientific simulation) as mentioned in this paper is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision that are based on multiresolution analysis and separated representations.

TL;DR: In this paper , the authors proposed a regularization algorithm for ill-posed linear inverse problems based on the Fredholm integral equation of the first kind (RKHS), and proved that the RKHS-regularized estimator has a mean-square error converging linearly as the noise scale decreases, with a multiplicative factor smaller than the commonly-used $L 2 -regularizer.

TL;DR: SpanReg as discussed by the authors is a regularization method for the solution of the Fredholm integral equation of the first kind, in which they incorporate solutions corresponding to a range of Tikhonov regularizers into the end result.

TL;DR: In this article , the forward problem is formulated as a minimization problem of a least-square misfit function with the (IBVP) as the constraint, and the adjoint problem is derived to computed the direction of steepest descent in the iterative process for minimization.